Washington -LRB- CNN -RRB- -- The chairman of the Republican Party and a leading GOP senator called on Senate Majority Leader Harry Reid to give up his post Sunday , following the publication of remarks he made about President Obama 's race in 2008 .

A new book quotes Reid , D-Nevada , as saying privately in 2008 that Obama could be successful as a black candidate in part because of his `` light-skinned '' appearance and speaking patterns `` with no Negro dialect , unless he wanted to have one . ''

The remarks were `` embarrassing and racially insensitive , '' said Sen. John Cornyn , R-Texas , head of the GOP 's Senate campaign arm , in a statement to CNN .

GOP Chairman Michael Steele , on NBC 's `` Meet the Press , '' said : `` Racism and racist conversations have no place today in America . ''

Steele also was on the defensive for a remark he made last week that members of both parties have called a racial slur . In an interview with Fox News , Steele used the phrase `` honest injun . ''

The Congressional Black Caucus has accepted Reid 's apology and is dismissing calls for him to step down as majority leader .

Rep. Barbara Lee , chairwoman of the caucus , issued the following statement : `` I have had an opportunity to speak with Senator Reid and he apologized for his unfortunate remarks concerning the president , and he understands the gravity of such remarks . There are too many issues like the economy , job creation and energy for these regrettable comments to distract us from the work that must be done on behalf of the American people . ''

Democrats also rejected the calls for Reid 's dismissal . Gov. Tim Kaine of Virginia , chairman of the Democratic Party , said `` the case is closed '' following Reid 's round of apologies .

Douglas Wilder of Virginia , who 20 years ago became the nation 's first elected African-American governor , also rejected calls for Reid 's ouster .

`` I think that what Reid was giving was a personal opinion , which was n't affecting the laws or the operation of the dispensation of justice in our country , '' Wilder told CNN 's `` State of the Union . ''

But he said he believes the incident `` illustrates the need for more open discussion about race . ''

Reid 's office made clear he has no plans to step down .

Democrats rejected the calls for Reid 's dismissal , and Reid 's office made clear he has no plans to step down .

`` Sen. Reid will stay in his position as majority leader and will run for re-election , '' his spokesman said .

`` As the leader in the fight to pass the Voting Rights Act and legislation banning hate crimes , Sen. Reid has a long record of addressing issues that are important to the African-American community . His Republican critics who are looking to politicize the issue ca n't say the same . ''

Reid 's controversial quote is in the book `` Game Change , '' due in stores Monday . The authors write that `` Reid was convinced , in fact , that Obama 's race would help him more than hurt him in a bid for the Democratic nomination . ''

In a statement to CNN , Reid said , `` I deeply regret using such a poor choice of words . ''

`` I sincerely apologize for offending any and all Americans , especially African-Americans for my improper comments . I was a proud and enthusiastic supporter of Barack Obama during the campaign and have worked as hard as I can to advance President Obama 's legislative agenda , '' Reid said .

In his defense , he pointed to his efforts to integrate the Las Vegas strip and the gaming industry , among other legislation favored by African-American voters .

`` I have worked hard to advance issues important to the African-American community , '' he said .

And the senate leader called Obama on Saturday afternoon to apologize for the remarks . In a statement issued after the call , Obama said , `` As far as I am concerned , the book is closed . ''

`` Harry Reid called me today and apologized for an unfortunate comment reported today , '' the president said . `` I accepted Harry 's apology without question because I 've known him for years , I 've seen the passionate leadership he 's shown on issues of social justice and I know what 's in his heart . ''

An aide to the senator told CNN that Reid also offered apologies to several prominent African-American political figures , including House Democrats Jim Clyburn of South Carolina and Barbara Lee of California ; the Rev. Al Sharpton ; CNN political contributor and Democratic strategist Donna Brazile ; NAACP chairman Julian Bond ; and the head of the Leadership Conference on Civil Rights , Wade Henderson .

Steele , the GOP 's first African-American chairman , was asked about the remarks on both `` Meet the Press '' and `` Fox News Sunday . '' He told NBC on Sunday he believes Reid is out of touch with `` how African-Americans generally feel '' about sensitive issues .

Steele was asked by NBC whether he believes the situation is similar to one involving former Sen. Trent Lott , who lost his post as Senate majority leader in 2002 after saying that the nation would have been better off if one-time segregationist candidate Strom Thurmond had been elected president .

`` Oh , yeah . There is a big double standard here , '' Steele said on NBC .

Steele added : `` When Democrats get caught saying racist things , you know , an apology is enough . ''

Steele said that if a Republican senator had made the same remark Reid did , Steele himself and the Democratic Party `` would be screaming for his head very much as they were with Trent Lott . ''

Cornyn , in his statement , also accused Democrats of following a `` double standard , '' and noted that they had pushed Lott to step down .

`` As we await his explanation , Sen. Reid should do the right thing , follow the example that he himself set in 2002 , and step down as majority leader , '' Cornyn said .

Kaine shot back against those arguments .

`` Anybody looking at Trent Lott 's statements praising somebody who had been a pro-segregation candidate for president will see that there is no comparison between those comments and those of Sen. Reid , '' Kaine told NBC .

The comments `` were in the context of praising the senator and acknowledging that the senator could be a great president , but they were still insensitive , '' Kaine said .

Asked whether Reid should resign , he said , `` Absolutely not . ... We 're moving on . ''

Nevada state Senate Majority Leader Steven Horsford , who is African-American , affirmed his support for Reid in a statement Saturday .

`` While I am disappointed in Sen. Reid 's comment and choice of words , I accept his apology , '' said Horsford , a Democrat . `` I have known Sen. Reid for many years and he has consistently been supportive of advancing the interests of the African-American community as he has for all Nevadans and all Americans . ''

Steele , meanwhile , was asked about his remark in a Fox News interview last week that the GOP platform `` is one of the best political documents that 's been written in the last 25 years , ` honest injun ' on that . ''

`` Fox News Sunday '' host Chris Wallace noted that lawmakers from both parties have called that a racial slur .

`` Well , if it is , I apologize for it . It 's not an intent to be a racial slur . I was n't intending to say a racial slur at all , '' Steele said .

CNN 's Dana Bash , Mark Preston and Rebecca Sinderbrand contributed to this report .

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NEW : Congressional Black Caucus rejects calls for Reid to step down

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Michael Steele calls for Reid to step down , accuses Dems of `` double standard ''

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GOP chair says Senate majority leader 's language `` harkens back to the 1950s and '60s ''

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New book quotes Reid discussing `` light-skinned '' Obama 's lack of `` Negro dialect ''